My house is plumbed with PEX. If I go with PEX then there is the expense of the necessary tools to "crimp" the joints, or use SharkBite type fittings (allowed by code, but not encouraged). What makes sense for adding the bath in my basement? Working with PEX should be easy for my project, existing 3/4 inch supply lines are running close by overhead. I am concerned about the push type PEX fittings, and the expense of getting the right tools to crimp if I go that route. Does it make any sense to add these new supply lines in copper, how would it be done?

Pros: If you have an extra moment, take a look at my other thread: "Basement Plumbing Rough In (with photo)" and give your opinion/advice about venting the tub...

I would not use a Sharkbite or a compression fitting inside a wall space. You can rent the crimpers for PEX tubing. Even if you switch to copper there will be at least two PEX connections that must be made.